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Almost sure invariance principle for some maps of an interval

Published online by Cambridge University Press:  19 September 2008

Krystyna Ziemian
Krystyna Ziemian
Affiliation:
Instytut Matematyki, Uniwersytet Warszawski, PKiN IXp, 00-901 Warszawa, Poland
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Abstract

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We prove an almost sure invariance principle and a central limit theorem for the process , where f is a map of an interval with a non-positive Schwarzian derivative whose trajectories of critical points stay far from the critical points, and F is a measurable function with bounded p-variation (p ≥ 1).

The almost sure invariance principle implies the Log-log laws, integral tests and a distributional type of invariance principle for the process .

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 5 , Issue 4 , December 1985 , pp. 625 - 640
Copyright
Copyright © Cambridge University Press 1985

References

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